The production of Quarkonia states at hadron colliders has been the subject of various theoretical approaches, which can now be compared to measurement performed at LHC. In the Charmonium family, the production of J/Psi has been studied over wide range of pT. In the Bottomonium family, the production of Y(1S) has been studied by ATLAS. The recent first observation of resonances decaying to Y(1S) gamma and Y(2S) gamma, and with mass about 30 MeV below the open-beauty threshold is presented. The signal is consistent with the multiplet of Chi_b(3P) states predicted by potential models. Comparable studies in the Charmonium sector and plans for future measurements are illustrated